Upper BH mass limit, another structure formation clue?

This paper makes the case for an upper mass limit of about 10 billion solar, for black holes. Their central black holes may help galaxies to form and may be important to understanding structure formation---an outstanding problem in cosmology.

The mass limit is proposed tentatively and requires further confirmation. The paper in question has been accepted for publication in the Monthly Notices of the Royal Astronomical Society (MNRAS).

"We make a case for the existence for ultra-massive black holes (UMBHs) in the Universe, but argue that there exists a likely upper limit to black hole masses of the order of [tex]M \sim 10^{10} \msun[/tex]. We show that there are three strong lines of argument that predicate the existence of UMBHs: (i) expected as a natural extension of the observed black hole mass bulge luminosity relation, when extrapolated to the bulge luminosities of bright central galaxies in clusters; (ii) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger-induced accretion inevitably leads to the existence of rare UMBHs at late times; (iii) the local mass function of black holes computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at z = 0. Consistency between the optical and X-ray census of the local black hole mass function requires an upper limit to black hole masses. This consistent picture also predicts that the slope of the [tex]M_{\rm bh}[/tex]-[tex]\sigma[/tex] relation will evolve with redshift at the high mass end. Models of self-regulation that explain the co-evolution of the stellar component and nuclear black holes naturally provide such an upper limit. The combination of multi-wavelength constraints predicts the existence of UMBHs and simultaneously provides an upper limit to their masses. The typical hosts for these local UMBHs are likely the bright, central cluster galaxies in the nearby Universe."

I think it's an informative paper, given how little seems to be known about the specific subject.

There are a couple of points I wish they were more specific about. First, they mention several theories whereby the accretion of dust into the SMBH causes an outward flow of particles or radiation out to some radius, which prevents additional gas from accreting from outside that radius. This cuts off the "fuel supply" for further accretion.

But it seems logical that once the accretion subsequently nearly stops, the outward flow of particles or radiation must also nearly stop, thereby allowing additional dust to accrete inwards and resume the BH growth. Apparently the evolution of these galaxies must be such that at some stage they become more stabilized, e.g. through pervasive star formation, such that velocity dispersion in the halo decreases over time. This would then be a secondary mechanism for cutting off the SMBH's future growth and establishing an absolute upper limit of mass.

They also mention that these large galaxies typically were formed through multiple galactic mergers, maybe around 100 mergers each. One might expect such collisions to increase the chaotic motions inside the merged galaxy, breaking down any then-existing stable barriers to BH growth, such that the limiting process needs to re-establish itself and burn through a newly reformed gas supply bubble. One might speculate that if such mergers continue indefinitely (at an ever slowing rate), any absolute upper limit on SMBH mass could eventually be circumvented. Seems like a scenario they should mention in their model, or explain why not. They do seem to apply their SMBH mass upper limit prediction only as far as the z=0 era.

Thanks for the comments. Another variable they deal with is efficiency---the fraction of gravitational energy that is converted to radiation or other output---and I think their model assumes efficiency increase over time. The model starts at some time far back in the past---large z---and extends up to the present---namely z = 0.

"Priya, and her co-authors, show fairly convincingly that black holes are hard to feed to bloating and that the black hole mass maxes out at a nice 10 billion or so solar masses, and that there are ultramassive black holes out there that mass more than the one in M87 but no more than about 10 billion solar mass black holes."